Analogical and inductive reasoning

Abstract

The first problem discussed in this thesis is the logical problem of analogy, which, given a formal definition of analogical inference, asks under what conditions such inferences may be justified. By showing the inadequacy of approaches based on the degree of similarity between analogues, the importance of relevance between known and inferred similarities is highlighted. The need for a logical semantics for relevance motivates the definition of determinations, first-order expressions capturing the idea of relevance between predicate schemata. Determinations are shown to justify analogical inferences and single-instance generalizations non-trivially, and to express an apparently common form of knowledge hitherto overlooked in knowledge-based systems. Analogical reasoning is implemented in MRS, a logic programming system, and shown to be more efficient than simple rule-based methods for some important inference tasks. The ability to acquire and use determinations is shown strictly to increase the inferences a system can make from a given set of data. Programs are described for the inductive acquisition of determinations and their subsequent use in analogical reasoning to aid in the construction of a large knowledge base. The second problem, suggested by and subsuming the first, is to identify the ways in which existing knowledge can be used to help a system to learn from experience. A method is given for enumerating the types of knowledge, of which determinations are but one, that contribute to learning, and a general inductive inference machine is described based on these ideas. The application of a logical, knowledge-based approach to the problems of analogy and induction thus shows the need for a system to be able to detect as many logical forms of regularity as possible in order to maximize its inferential capability. The possibility that important aspects of 'common sense' are captured by complex, abstract regularities suggests further empirical research to identify this knowledge.